X11, Wayland and WDDM only use the bare minimum functionality from those APIs, so they work just fine on old DX9-level GPUs for example. Godot needs much more recent GPUs.
It's the use case that requires the bare minimum functionality. Godot might require more recent lower-level APIs than the other GUI toolkits, but if the use cases are similar, then it wouldn't require more performance out of them than the other GUI toolkits would. Using software-based implementations of those APIs would more than likely be sufficient, meaning that there's no dependence on any specific class of GPU.
